Page 160 - ADVANCED MATH F.5

Form Five Form Five

share alternative methods of deriving the formula for implicit
differentiation of implicitly defined functions.
3. Use Examples 8.15, 8.16, and 8.17 in the Student’s Book to
guide students and assist them in finding solutions to the given
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problems by using implicit differentiation. Allow students to
share alternative methods of finding solution by the quotient
rule. Engage them in using mathematical software and scientific
calculators, to verify the solution of the given Examples.

4. Instruct students to attempt Exercise 8.6 in the Student’s Book.
Advise students to submit their work; check the correctness
of their answers, and provide them constructive feedback.
Encourage students to explore additional resources, such as
online tutorials, Symbolab, Mathematica, or reference books
to enrich their understanding and for further practice.

Answers to Exercise 8.6

dy dy 5
1. (a) 3y 2 (b) 1+ 3.
dx dx 2(x − 2)(x + 3)

108 ( x + ) 2 3 2 2
4. 7. 8.
3 25(3x + 6) 4 4 3
x 4
9. y′= 10. z′ =±
2
3x − 27 3

Further implicit differentiation of functions
Teaching steps
1. Assist students through discussion to differentiate expressions
without rearranging the terms of the expression. Lead them
to differentiate each terms by applying the chain rule and the
product rule.

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Mathematics for Advanced Secondary Schools

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